A definition of an abelian group is provided along with examples using matrix groups. The general linear group and the special linear group are introduced.
For closure, I thought you had to show if A and B are in G, then AB is also in G? then can't you say that det A and det B are non zero, so det(AB)=det(A) det (B), which is non zero, so AB is invertible, which means AB is also in G?
The set of all nxn matrices with real entries under matrix multiplication. There you have said that the multiplication of (0 0) (1 0) should give the identity matrix. Actually matrix (0 0) (0 1) AI = A so there is no problem with that. where I is identity matrix. If am wrong plz correct me.
